On a most elementary level, the flow stress of a dislocated crystal can be related to the density and arrangement of crystal lattice dislocations. This is well established since the seminal paper of Taylor [1]} who analyzed crystal plasticity in terms of the motion of dislocations and established a fundamental relationship between the flow stress \(\tau _{\rm f}\)  – here understood as critical resolved shear stress on the active slip system(s) – and the density of dislocations \(\rho \) . , \(\tau _{\rm f} = \alpha \mu b \sqrt{\rho }\)  where \(\mu \)  is the shear modulus, \(b\)  the length of the Burgers vector of the active slip systems, and \(\alpha \)  a numerical factor which was put by Taylor into the range of \(\alpha \approx 0.2...0.3\)  where it has remained ever since. However, while the structure of the Taylor relationship has never been in question, the precise nature of the dislocation arrangements that give rise to this dependency has been a subject of controversy for decades. Taylor considered a checkerboard pattern of positive and negative dislocations ('Taylor lattice') - an arrangement which, while analytically tractable, has the disadvantage that it has never been observed in experiment. Based on surface observations (blocking of slip lines), Mott and Seeger [2]}, [3]} proposed that the Taylor stress is produced by large pile ups of dislocations at indestructible Lomer-Cottrell Barriers, an idea which, while consistent with surface observations, cannot be reconciled with TEM where such pile ups are very hard to find. Bayley and Hirsch [4]} instead suggested that Taylor's law can be explained by the stress needed to cut forest dislocations, whose spacing scales like the square root of dislocation density. Finally, Hirsch and Warrington [5]} pointed out that Taylor-type behavior can also be explained by the dragging of jogs whose spacing in turn reflects the forest spacing.
